Transcript Public Goods

Chapter 4:
Public Goods
Econ 330: Public Finance
Dr. Reyadh Faras
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Definition of A Public Good
Once it is provided, the additional resource cost
of another person consuming the good is zero,
which means that consumption is nonrival.
To prevent anyone from consuming the good is
either very expensive or impossible, which
means that consumption is nonexcludable.
In contrast, consumption of a private good is
rival and excludable.
Impure public good is a good that satisfies either
condition.
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 Even though everyone consumes the same quantity of
the good, consumption is not valued equally by all.
 Classification as a public good depends on market
conditions and the state of technology.
 Private goods are not necessarily provided
exclusively by the private sector.
 Public goods are not necessarily provided exclusively
by the public sector.
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Types of Goods
RIVAL
YES
EXCLUDABLE
YES
NO
NO
NATURAL
PRIVATE
MONOPOLY
GOODS
COMMON
PUBLIC
RESOURCES GOODS
Efficient Provision
Private Goods
 Market demand is a horizontal summation of quantities
consumed by all consumers.
 Equilibrium is reached where supply equals demand at
quantity ____ and price _____ .
 Adam consumes _____ units and Eve consumes ____
units.
 Note that there consumption does not have to be equal,
why?
 At equilibrium, resource allocation is pareto efficient:
A utility maximizing individual sets the marginal rate
of substitution of the two goods equal to the price ratio
of the two goods: MRSfa = Pf / Pa
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Efficient Provision of Private Goods
Eve (DfA)
$11
Adam
(DfA)
5
1
Market
(DfA+E)
6
$9
7
3
10
$7
9
5
14
$5
11
7
18
$3
13
9
22
$1
15
11
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Price
$
12
11
10
Sf
9
8
7
6
5
4
3
DfA+E
2
1
DfE
0
0
1
2
3
4
5
6
7
8
DfA
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Quantity of Pizza
 Set Pa= $1, this reduces the condition to:
MRSfa = Pf
 Adam and Eve both set MRS = ____
 Producers set the marginal rate of transformation
MRTfa = ____
 At equilibrium, MRSAfa = MRSEfa = MRTfa , which
is the condition for pareto efficiency.
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A. Deriving the Efficiency Contribution
 Public Goods
 Assume Adam and Eve watch a firework show
consists of 19 rockets and each extra rocket costs
$5.
 Adam is willing to pay $6 for the extra rocket,
while Eve is willing to pay $4.
 Question, is it efficient to expand the size of the
show by one extra rocket?
 Answer, we need to compare the marginal
________ to the marginal ________.
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Efficient Provision of Public Goods
Units of Fireworks
1
2
3
4
Adam (DrA)
$300
$250
$200
$150
Eve (DfE)
250
200
150
100
Market
(DfA+E)
$550
$450
$350
$250
$
800
750
700
650
600
550
500
450
Sr
400
350
300
250
200
150
DrA+E
DrA
100
50
0
DrE
1
2
3
Quantity of
Fireworks4
 Because consumption is nonrival, the 20th rocket is
consumed by both.
 Hence, the marginal benefit of the 20th rocket is the
sum of what they are willing to pay, which is $____.
 Because the marginal cost is $5, it is worthy to
consume the 20th rocket.
 Generally: if the sum of individuals' willingness to
pay for an additional unit of a public good exceeds its
marginal cost, efficiency requires that the unit be
purchased; otherwise it should not.
 Efficiency requires that provision of a public good be
expanded until reaching the level at which the sum of each
person's marginal valuation on the last unit just equals the
marginal cost.
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 Efficiency is reached at the point where Adam's and
Eve's willingness to pay for an additional unit just
equals the marginal cost of producing a unit.
 Graphically, the marginal cost schedule, S, is
superimposed on the group willingness to pay
curve, DA+E.
 The intersection occurs at quantity 45 and marginal
cost $6.
 At equilibrium, MRSAra + MRSEra = MRTra , which is
the condition for pareto efficiency.
 For a public good, market demand is found by vertical
summation of individual demand curves.
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Note:
 For a private good, everyone has the same MRS, but
people can consume different quantities.
 Therefore, demands are summed horizontally over the
differing quantities.
 Individuals see the same price and then decide what
quantity they want.
 For a public good, everyone consumes the same
quantity, but people can have different MRS.
 Therefore, vertical summation of quantities is
required to find the group willingness to pay.
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 Everyone sees the same quantity and then decide
what price they are willing to pay.
 Problem: People have incentives to hide their true
preferences for public good in order not to pay for it.
 This is called the free rider problem, which results
in a shortage in the supply of public goods (below the
efficient amount).
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 Solution: suppose 1) each person's demand curve is
known, and 2) transferability of the good to another
person is impossible, then each person is charged a
price based on its willingness to pay, this is called
perfect price discrimination.
 Conclusion:
Since knowledge of individual preferences is
impossible, private provision leads to
inefficiency (even if a nonrival good is excludable).
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B. The Free Rider Problem
 Some suggest as a solution to the free rider problem
that the government provides the public good.
 The government is able to find everyone's preference
and then use its coercive power to force everyone to
pay.
 Free ridership is based on the hypothesis that people
maximize a utility function that depends only on their
own consumption.
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The Privatization Debate
 Definition: Privatization means taking services that
are supplied by the government and turning them
over to the private sector for provision and/or
production.
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A. Public Versus Private Provision
 Some services provided by publicly provided goods
can be obtained privately.
 Examples: Protection (private policemen are 3 times
public ones) and dispute settlement (40,000 cases are
solved privately).
 Historically, in the 17th century many services were
provided privately, than now.
 However, recent trends are towards private provisions
in many communities.
 What is the right mix of public and private provision?
What criteria used to select inputs?
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 There are several considerations:
1. Relative wage and materials costs: the less
expensive sector is preferred on efficiency
grounds.
2. Administrative costs: under public provision,
fixed administrative costs are spread over a large
group of people.
3. Diversity of Tastes: with diversity, private
provision is more efficient because consumption
can be fitted into tastes.
4. Distributional issues: community's notion of
fairness requires the availability of some goods to
everyone.
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B. Public Versus Private Production
 Even with the agreement of providing goods publicly,
disagreement may arise over whether they should be
produced publicly or privately.
 This is due to differences regarding:
1) the role of government in the economy.
2) the relative costs of public and private production.
 Little systematic evidence exists on the cost
differences between private and public production
because of differences in quality of services provided
by each.
 Opponents of privatization argue that private
contractors produce inferior goods.
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 Response:
1) The government writes a contract that specifies
the level of desired quality,
2) Consumers switch to better quality producers,
3) Reputation makes private producers worry
about quality in order to get future contracts.
4) Market environment matters. For example, a
privately owned monopoly may produce
inefficiently, while a public producer facing a lot
of competition may produce efficiently.
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